Question: Simplify the following expression: $ z = \dfrac{4k + 4}{9k} - \dfrac{3}{10} $
Solution: In order to subtract expressions, they must have a common denominator. Multiply the first expression by $\dfrac{10}{10}$ $ \dfrac{4k + 4}{9k} \times \dfrac{10}{10} = \dfrac{40k + 40}{90k} $ Multiply the second expression by $\dfrac{9k}{9k}$ $ \dfrac{3}{10} \times \dfrac{9k}{9k} = \dfrac{27k}{90k} $ Therefore $ z = \dfrac{40k + 40}{90k} - \dfrac{27k}{90k} $ Now the expressions have the same denominator we can simply subtract the numerators: $z = \dfrac{40k + 40 - 27k }{90k} $ Distribute the negative sign: $z = \dfrac{40k + 40 - 27k}{90k}$ $z = \dfrac{13k + 40}{90k}$